•A novel solution approach for nonlinear multi-dofs dynamic response is proposed, in which both stable and unstable solutions are considered.•A coupled modeling for composite structures with micro-voids in complex multi-physics fields is presented.•Nonlinear multiple internal resonances and bifurcations of FG piezoelectric shells are studied.•The influence of key parameters on nonlinear amplitude-frequency response curves is discussed. This paper develops a new solution approach to solve nonlinear forced vibrations of functionally graded (FG) piezoelectric shells in multi-physics fields. The FG piezoelectric shells are subjected to electric-thermo-mechanical loads, and the effect of micro-voids is considered here. Motion equations are obtained by using Hamilton's principle, and combining with the Donnell nonlinear shallow shell theory. Afterwards, a new method combining multi-mode Galerkin scheme and Pseudo-arclength continuation method is used to solve the nonlinear multiple internal resonances and bifurcations of the multi-degree-of-freedom systems. The novel feature of this approach is that it can efficiently obtain the unstable solution and tackle the difficult problems in mathematics encountered during formulation. The results show that the external applied voltage, temperature change, external excitation, power-law exponent, and porosity volume fraction play important roles on nonlinear vibration response and bifurcation analysis of FG piezoelectric shells with micro-voids. Display omitted